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Find a 2x2 matrix A such that det(A)=3. (You must show why det(A)=3.) True or False: If A is an nxn matrix and has n pivot columns, then A is linearly independent. (You must justify your answer.) Give an example of a 4x4 matrix A such that Nul(A) does not equal the set containing the zero vector. Prove that for a pxq matrix C, the column space of C is a subspace of RP. (This needs to be a formal proof.)

Find a 2x2 matrix A such that det(A)=3. (You must show why det(A)=3.) True or False: If A is an nxn matrix and has n pivot columns, then A is linearly independent. (You must justify your answer.) Give an example of a 4x4 matrix A such that Nul(A) does not equal the set containing the zero vector. Prove that for a pxq matrix C, the column space of C is a subspace of RP. (This needs to be a formal proof.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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• Find a 2x2 matrix A such that det(A)=3. (You must show why det(A)=3.) • True or False: If A is an nxn matrix and has n pivot columns, then A is linearly independent. (You must justify your answer.) • Give an example of a 4x4 matrix A such that Nul(A) does not equal the set containing the zero vector. • Prove that for a pxq matrix C, the column space of C is a subspace of RP. (This needs to be a formal proof.)
Transcribed Image Text:• Find a 2x2 matrix A such that det(A)=3. (You must show why det(A)=3.) • True or False: If A is an nxn matrix and has n pivot columns, then A is linearly independent. (You must justify your answer.) • Give an example of a 4x4 matrix A such that Nul(A) does not equal the set containing the zero vector. • Prove that for a pxq matrix C, the column space of C is a subspace of RP. (This needs to be a formal proof.)
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